codeforces-632A-Grandma Laura and Apples

632A-Grandma Laura and Apples

                time limit per test1 second     memory limit per test256 megabytes

Grandma Laura came to the market to sell some apples. During the day she sold all the apples she had. But grandma is old, so she forgot how many apples she had brought to the market.

She precisely remembers she had n buyers and each of them bought exactly half of the apples she had at the moment of the purchase and also she gave a half of an apple to some of them as a gift (if the number of apples at the moment of purchase was odd), until she sold all the apples she had.

So each buyer took some integral positive number of apples, but maybe he didn’t pay for a half of an apple (if the number of apples at the moment of the purchase was odd).

For each buyer grandma remembers if she gave a half of an apple as a gift or not. The cost of an apple is p (the number p is even).

Print the total money grandma should have at the end of the day to check if some buyers cheated her.

Input
The first line contains two integers n and p (1 ≤ n ≤ 40, 2 ≤ p ≤ 1000) — the number of the buyers and the cost of one apple. It is guaranteed that the number p is even.

The next n lines contains the description of buyers. Each buyer is described with the string half if he simply bought half of the apples and with the string halfplus if grandma also gave him a half of an apple as a gift.

It is guaranteed that grandma has at least one apple at the start of the day and she has no apples at the end of the day.

Output
Print the only integer a — the total money grandma should have at the end of the day.

Note that the answer can be too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.

input
2 10
half
halfplus
output
15

input
3 10
halfplus
halfplus
halfplus
output
55

题目链接:cf-632A

题目大意：有一个老太太卖苹果，一天有n个人来买，每个苹果p元钱。初始苹果数量未知，每个人购买的时候，总是购买剩下苹果的一半，
1. 如果剩下苹果是奇数，则买完一半老太太会把另半个苹果送给他。即halfplus
2. 如果剩下苹果是偶数，即half

题目思路：倒推先求出苹果的初始数量。首先我们可以确定，最后一个人购买一定是只剩下1个苹果了。往前推，如果前面一个人是half说明前面为偶数，如果是halfplus则为奇数

以下是代码：

#include <bits/stdc++.h>
#define mst(a) memset(a,0,sizeof (a))
#define FOR(i,n) for (int i = 0; i < n; i++)
#define INF 1e9
#define eps 1e-10
using namespace std;

typedef long long ll;
long long ret[50];
int main(){
    int n,p;
    cin >> n >> p;
    long long ans = 1,tmp = 0;
    for(int i = 0; i < n; i++)
    {
        string s;
        cin >> s;
        if (s == "half") ret[i] = 1;
        else ret[i] = 2,tmp++;
    } 
    for (int i = n - 2; i>= 0; i--)
    {
        if (ret[i] == 1) ans = ans * 2;
        else ans = ans * 2 + 1;
    }
    ans = ans * p - tmp * (p / 2);
    cout << ans << endl;
    return 0;
}